Van der Waal repulsion and Lennard Jones potential

[LCSphysicist]

Hello there. Do you know any paper that derive the Lennard Jones potential $V = \epsilon [(\delta / r)^{12}-2(\delta / r)^6]$ theorically? If you know a book instead, let me know. Thank you

 

[Astronuc]

Apparently, J E Lennard-Jones discusses some details in an article entitled, Cohesion, in the Proceedings of the Physical Society (1926-1948)
https://iopscience.iop.org/article/10.1088/0959-5309/43/5/301 (must be purchased or accessed through one institution)

Otherwise, one can find notes in various university or academic lectures.
https://chem.libretexts.org/Bookshe...Specific_Interactions/Lennard-Jones_Potential

https://chem.libretexts.org/Bookshe...cific_Interactions/Dipole-Dipole_Interactions

The Wikipedia article seems consistent with some academic notes I reviewed.
https://en.wikipedia.org/wiki/Lennard-Jones_potential#Physical_background_and_mathematical_details

 

[TeethWhitener]

The $\frac{1}{r^{12}}$ portion is not physical--it's just a numerically convenient way to approximate a rapidly increasing function. It's a vestige from a time when computers were much much slower.

The $\frac{1}{r^6}$ portion comes from treating the dipole-dipole interaction perturbatively to second order. This is actually the short-distance limit of the full interaction, not taking into account retardation effects. The full derivation in all its gory details of both short (London) and long (Casimir-Polder) limits is given in "Molecular Quantum Electrodynamics" by Craig and Thirunamachandran (p. 152ff): https://www.google.com/books/editio...rpbdozIZt3sC?hl=en&gbpv=1&printsec=frontcover

 

[Demystifier]

The $\frac{1}{r^6}$ portion comes from treating the dipole-dipole interaction perturbatively to second order. This is actually the short-distance limit of the full interaction, not taking into account retardation effects. The full derivation in all its gory details of both short (London) and long (Casimir-Polder) limits is given in "Molecular Quantum Electrodynamics" by Craig and Thirunamachandran (p. 152ff): https://www.google.com/books/editio...rpbdozIZt3sC?hl=en&gbpv=1&printsec=frontcover

A derivation can also be found in the 3-volume QM textbook by Cohen-Tannoudji, Diu and Laloe, Chapter XI.C.